Mathematical Art

Sarah Stengle

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Math Art Workshop January 6, 2018Author of this blog post, artist Sarah Stengle will teach a Math Art Workshop from 10 a.m. to 12 noon on January 6, 2018, at the Center for Art and Dance, which is in the same building as the Flaten Art Museum. Everyone is welcome to attend. Further information can be found here.

Seeing Math at Flaten Art Museum at St. Olaf College, in Northfield, Minnesota, is a masterfully curated interdisciplinary exhibit featuring six contemporary artists who are clearly comfortable working creatively with mathematical concepts. Curator Taylor Davis selected works by Daniel Dean, Tracy Krumm, Emily Lynch Victory, Ben Moren, Margaret Pezalla-Granlund, and Roman Verostko that span a wide range of media, from video through painting to fiber art. The works incorporate mathematical topics such as algorithms, infinity, geometry, counting systems, and the fourth dimension.

Emily Lynch Victory, P1: Number System Base 16, 2016

Emily Lynch Victory’s P1: Number System Base 16 is a complex set of grids of linear marks that resemble scraffito. At a distance her work appears to be an imposing minimalist painting with a densely worked surface. Upon closer examination the grid turns out to be a visual mapping of numbers expressed in different base systems. Visitors can appreciate the beauty of the accumulated markings with or without unraveling the system of numerical notations that generated the imagery.

Daniel Dean, Infinity, 2015

At first glance, Infinity, by Daniel Dean, also closely resembles a minimalist work of art. The pristine construction and electric blue glow are reminiscent of Donald Judd’s light sculptures. The title Infinity combined with the circular motion of the light can be interpreted as metaphor for the cycle of life. But the image in the lighted panels is a painfully familiar one: the one that appears when our computer gets stuck in processing a task. Dean plays with the sublime notions of infinity and light using an image that is also an everyday symbol of frustration, an image that simultaneously evokes the feeling of things taking “forever” while waiting around in the prosaic realm of electronic dysfunction.

Ben Moren, River Suspension, (Analysis), 2015

Ben Moren’s video installation River Suspension (Analysis) captures multiple images of the artist apparently hovering in mid-air over a river. The effect is starkly surreal. Using a very high-speed camera developed by the military for analyzing the trajectory of ballistic weapons, he instead tracks the trajectory of his own leaping body. The frames are so numerous that motion is nearly frozen, confounding our sense of time and gravity. Usually talk about the trajectory of an artist is in reference to a career path, not the physical body of the artist in motion. Moren elicits a complex emotional response to his fairly simple action, jumping, by modeling his trajectory physically and technically in a context where one expects pure metaphor.

This highly engaging exhibit also includes examples of book art, fiber art, algorithmic art and models of tesseracts (cubes imagined in the fourth dimension). Attendees who linger will be rewarded both by the masterful work exhibited and by the varied depth of information provided. The text panels are unusually well written, and additionally there is a table with an array of enjoyable mathematical puzzles, models, and books.

Seeing Math is on view through January 15, 2018, at Flaten Art Museum, St. Olaf College, Northfield, Minnesota. It is inspired by works of mathematically themed art acquired with The Arnold Ostebee ’72 and Kay Smith Endowed Fund for Mathematical Art. Established in 2014, this fund supports the acquisition and display of mathematically themed art at St. Olaf College. The museum will be closed during winter break, December 10, 2017 through January 2, 2018.

Artist Eva Mantell applies meticulous attention to materials that are on the verge of being discarded. The resulting artwork is complex, highly ordered and the humble materials are lent a poetic weightlessness. The organizing principles that generate her constructs are deceptively simple. She sets rules or parameters, which when followed or repeated, produce complex results. Her studio production is process-driven in that the final result is not known at the start, but rather produced by intuitively following the simple rules she sets out for herself.

She likened her approach to art to Alan Turing’s approach to understanding the morphogenesis of flowers. Posing the question “How does a flower know how to become a flower?” Turing spent the last years of his mathematical career looking closely at ordinary flowers. His mathematical inquiry into biological morphogenesis worked with simple pairings of activators and inhibitors that behaved in predictable ways but produced complex results as they interacted over time. Similarly Ms. Mantell observes ordinary things, applies simple parameters to generate conceptually and aesthetically complex results in her artwork.

Cloud Map, torn magazine page, wax, 8 x 10″ 2017

With Cloud Map, Ms. Mantell started with a cigarette advertisement from a magazine. She imposed the restriction of using only her bare hands to create a drawing; no tools or other materials were used. Then she set out to remove as much material as possible while still retaining the structural integrity of the original sheet of paper. The results closely resemble Turing patterns. A torn hole could never be too large or the integrity of the underlying image would be destroyed; neither could the supporting matrix remain too thick or the challenge of removing as much material as possible would not have been met. Although the holes were torn in an intuitive manner, one could imagine that “completeness” was the inhibitor and “removing” was the activator.

There is an emotional quality to the act of removing. The substrate, already disposable, moves towards fragility. Being damaged while remaining recognizably whole has parallels with being ill or wounded and yet continuing to live. The sense of vulnerability is underscored by leaving only the nicotine warning intact and legible.

The touch of the hand is key to understanding the artwork. At first glance Nicotine appears to be a perforated and colorful lattice. Closer examination reveals the nearly disposable substrate and the patience evident in the handwork. The careful attention and repeated touching of the material elevates the sheet of paper out of the realm of rubbish into the realm of a carefully realized work of art. In this sense Ms. Mantell’s work is transformative, use mundane materials to reflect on the nature of transience.

This Little Palace, cut paper cup, wax, 8 x 8 x 5″ 2017

Another body of work was the project transforming discarded paper coffee cups into space filling sculptural objects. She set herself the challenge of making the cup occupy as much volumes as possible without either adding or removing materials. Many of the artist’s solution approach surface filling curves before being expanded into a elaborate brambles resembling tumbleweeds or feathers. Starting with a familiar object on the brink of its own extinction, she expands it to occupy more time, in the form of her careful attention to it, and space.

By exploring simple principles with a meditative and deeply human eye, Eva Mantell explores pattern in nature using materials that refer to our everyday lives. The patience and care with which she attends to disposable objects makes us question our relationship to the human detritus our culture thoughtlessly produces. Her work gently but clearly underscores the importance of noticing the overlooked and finding structure and beauty in the ephemeral.

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Eva Mantell: lives in Princeton, NJ and has exhibited her sculpture, painting and video at the Monmouth Museum, the Hunterdon Museum, the Bernstein Gallery at Princeton University, the Abington Art Center, the Jersey City Museum and the Brooklyn Museum of Art. She has a BA from Penn and an MFA from the School of Visual Arts in NYC. She curates, teaches and speaks about art including the recent Art as Activism, at the exhibit Fight or Flight at The Painting Center, NYC. She has a special interest in arts engagement and community outreach and her teaching has been included in Designing and Delivering Arts Programs for Older Adult Learners, published by the National Center for Creative Aging in Washington, DC. In January 2018, her work will be on view in a group exhibit in Brooklyn, NY at http://soho20gallery.com/ Eva’s website is evamantell.com.

Holger Hadrich makes complex, collapsible geometric structures out of steel wire, and then photographs them in a way that dissolves the pure determination of the geometry into a feeling of a fleeting memory. The context chosen is often an ordinary place that implies motion, or transition. Sidewalks, asphalt and rivers recur with the superimposition of a delicate geometric structure.

These objects rarely obscure their backdrop but rather hover like an apparition. One can see right through them, as one could see through a ghost. In his hands, the timeless geometry of the Archimedean solids are presented as movable objects that we pass by in a fleeting world. The context for his creations underscore the idea of passage and form a sequence of ordinary by-ways transformed by an ongoing internal conversation with mathematical form.

The objects themselves are based on polyhedra, which are usually conceived of as solid. In his hands, however, they are rendered flexible and collapsible. Their web-like delicacy show precision and immense patience. One can almost imagine the object being turned in hand as careful attention is paid to the vertices. In many cases they are punctuated by small brass washers or carefully formed loops, which form a secured but collapsible hub. A different aspect of the work is made apparent when the objects are held in the hands. They are designed to be collapsible. Many are collapsible along more than one axis. To understand the collapsibility of his constructs it is best to handle them or see them in motion. His video Medusa Tower below shows one of his structures expanding from a depth of about three inches to nearly five meters.

When asked about own his work, Hadrich’s response was essentially a mathematical one, and no doubt these forms are rooted in Plato, Aristotle and Johnson, but most mathematical art has text-book clarity and a purely digital manifestation. Hadrich’s images start with the hand eye connection and stainless steel wire. They move from linear clarity toward intentional atmospheric dissolve when photographed.

Art historians from Vasari to Wöfflin have debated the supremacy of linear versus painter pictorial devices in art. These works are both simultaneously linear and painterly (malerisch). The absolute clarity of the mathematic constructs is intentionally obscured to become integral to the partially dissolved, or transient clarity of the object as photographed. These linear forms become painterly through Hadrich’s lens. The geometric forms are pulled out of the originating mathematical abstractions and into our ordinary life, where they seem to hover on the brink of collapsing and disappearing.

To quote Wölfflin: “Composition, light and color no longer merely serve to define the form, but have their own life absolute clarity has been partly abandoned to enhance the effect.” The resolutely normal sidewalks and fragments of asphalt are also transformed when viewed through the orderly but complex web of geometric construction of wire. One immediately intuits a precise order that stands against our own transience and feels patient, quiet and timeless.
You can find more about Hadrich’s work on his Facebook page.

This is Sarah Stengle’s first contribution to this blog. Sarah is an artist and writer based in St Paul, Minnesota.

This year the huge Joint Mathematics Meeting was held in Atlanta Georgia with over 6,000 attendees. A section of the exhibition hall was turned into a gallery space to present art work with mathematical connections. There were also dozens of talks presented by both mathematicians and artists on the topic of Mathematical Art.

During one of these talks, Sarah Stengle presented work from her collaboration with Genevieve Gaiser Tremblay. The large series of works on paper, titled “Criterion of Yielding”, uses stereoscopic images from the 1850’s as the background for drawings of diagrams from the book “Mathematics of Plasticity” written by Rodney Hill in 1950.

The work “Criterion of Yielding, Winter Scene” features a mathematical schematic based on the deformation of metals that creates a visual bridge between the solitary figure on each side of the stereoscopic card. To enhance the feeling of antiquity, the artist uses ground peridot gemstone to make the pigment. This process gives the color a sense of stains instead of paint alluding to the paper as artifact.

The topic of plasticity revolves around the measurement of stress, strain, bending, and yielding. All these ideas are poetically associated to the human condition, both as individuals and with regards to our interactions. The layering of mathematical material over existing images presents an unexpected dichotomy. The additional process of pigmented staining and mark making instills each work with a sense of time.

Andrew James Smith developed a unique process of drawing regular polygons to create a spiral called a Protogon. The process to form a Protogon begins with a triangle and progresses with each new polygon sharing a side with the previous polygon and having one more side.

“Proto Pinwheel” is a digital study for a large acrylic painting and is a pigment transfer on wood. For this work Smith has started with a yellow opaque Protogon shape and then rotated 120 degrees and layered subsequent Protogon shapes in varying transparent colors. The result is a spiral pulsing with energy.

I look at a lot of art and I find quite a bit of work with Mathematical elements, but when I find new art inspired by a book of Mathematical proofs and figures I get really excited. Stengle’s new and ongoing series of drawings is based on Apollonius of Perga’s book “Conic Books I-IV”. Apolonius of Perga (262BC-109BC) was an ancient Greek geometrist who is famous for his innovated work in the mathematical field of conics. He explored the properties of conic sections and furthered our understanding of ellipses, parabolas, and hyperbolas.

Stengle has been collecting vintage postcards for a year. These postcards serve as the background image for her drawings. The choice of postcards is very important, as the artist looks for older non-glossy cards that can be drawn on. The subject matter on the card must also be fairly uninteresting visually so they can support but not over power Stengle’s mathematical imagery.

Each drawing is based on a proposition from “Conics Books I-IV”. There are three types of cards in this series. Some of the cards feature an accurate figure from a proposition in the book. In this case the book and proposition are written on the back of the card. Some of the other drawings have deviations from the figures in the book, but the aesthetics are interesting. Here the artist uses the work, and states the proposition and the fact there is a error on the back of the card. Finally, there are drawings that are imaginary propositions inspired by a particular figure.

“Perga Moraine Lake 72”

The card “Perga Moraine Lake 72” is the third type of card: it features an imaginary proposition. The artist had started to draw an Apolonius of Perga proof, but stopped at a point when the drawing reached a point of aesthetic completion. From the tip of the cone to its elliptical base, the mathematical figure leads the viewer’s eye from the mountain peaks in the landscape behind the lake to the shoreline.

“Post Card from Perga, Book 1, Proposition 2 Third Image”

This second Post card from Perga, “Book 1, Proposition 2 Third Image” shows the third of the four figures in the proposition. The background card is an overexposed photo card of a horse . The uneven quality of the card could be due to the fact it was probably made to promote the sale of the horse. This card features a figure drawn directly from the text with no changes. The axis of symmetry of the mathematical figure goes through the center of the animal.

“Lilac Conics Book 1 Proposition 4”

“Lilac Conics, Book 1 proposition 4” is also an accurate representation of the proposition in Apollonius of Perga’s book. The four conics are lined up along a beach mimicking the points of the masts of the fishermen’s boats.

Using carefully selected appropriated images as the backdrop for her geometric figures, Stengle has created a link between her mathematical subject matter and the world around us. The basis of the Perga post cards is an ancient text and the actual cards are vintage. When combined these elements lead to a sort of suspension of time. This series of work is a wonderful expression of the timeless aesthetics of Apollonius of Perga’s conic geometry.